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Full text of "Analytical Mechanics"

92. Kinetic Reaction.—The Law of Action and Reaction, which we found so useful in studying equilibrium, is applicable not only to problems of equilibrium but also to those of motion. In applying it to motion, however, we must •extend the meaning of the term " reaction;; so as to include a form of reaction which is known as kinetic reaction. In order to understand the nature of kinetic reaction consider the following ideal experiment:
Suppose you hold one end of a long elastic string, the other end of which is attached to a rectangular block placed upon a perfectly horizontal and smooth table. Let another person pull the block along the plane of the table and thereby stretch the string. While the string is being stretched you have to exert a force on it in order to keep your end of it fixed. At any instant the force with which you pull the string equals &nd is opposite to the force with which the string pulls your hand. The action equals the reaction and is oppositely directed. The same is true about the block and the person who holds it. What will happen if the block is released? Will the force which the string exerts on your hand cease as soon as the block is released? No. The string pulls on until it regains its natural length, something which does not take place instantaneously. The elasticity of the string urges it to assume its natural length. But this cannot be accomplished without moving the block. Therefore the string moves the block. But in order to start the block the string must exert a, force on it, and this in spite of the fact that the weight of